A December 2015 UK academic research paper on a persistent topic in policing and the authors state:
Our findings contradict long-standing beliefs among criminologists regarding the effectiveness of rapid response policing.....we argue that minimising response time is a highly effective policy in terms of apprehending a larger percentage of criminals
Link:http://poseidon01.ssrn.com/delivery.php?ID=5770951180880310830640920930780970 99035036062037000048094079104117119092081123105086 04501202805810705712510712201310200607002910607106 10170420101141201270941120800570460321270120090060 65105000098012113083072092029088089127075025120113 072121127066070&EXT=pdf

The Abstract:
Police agencies devote vast resources to minimising the time that it takes them to attend the scene of a crime. Despite this, the long-standing consensus is that police response time has no meaningful effect on the likelihood of catching offenders. We revisit this question using a uniquely rich data set from the Greater Manchester Police. To identify causal effects, we exploit discontinuities in distance to the response station across locations next to each other, but on different sides of division boundaries. Contrary to previous evidence, we found large and strongly significant effects: in our preferred estimate, a 10% increase in response time leads to a 4.6 percentage points decrease in the likelihood of detection. A faster response time also decreases the number of days that it takes for the police to detect a crime, conditional on eventual detection. We find stronger effects for thefts than for violent offences, although the effects are large for every type of crime. We identify the higher likelihood that a suspect will be named by a victim or witness as an important mechanism though which response time makes a difference.